Epilepsy Diagnosis Analysis via a Multiple-Measures Composite Strategy from the Viewpoint of Associated Network Analysis Methods

Abstract

Based on some typical complex network analysis methods and machine learning techniques, a general multiple-measures composited strategy-guided epilepsy diagnosis analysis framework is proposed in this brief paper. Five typical network analysis methods for biology time series analysis are utilized for real applications, including the classical visibility graph (VG), horizontal visibility graph (HVG), the limited penetrable visibility graph (LPVG), the modified frequency degree method (MFDM), and the quantity graph (QG). By using the aforementioned typical transformation methods, the EEG signal sets to be classified are transferred into graph network object sets. The main network features and related indicators are calculated and extracted as features for classification tasks. Some key features are selected via variance analysis, and the eXtreme Gradient Boosting (XGBOOST) machine learning algorithm is used for related binary and five-class classification tasks for electroencephalographic time series. Numerical experiments demonstrate that, through ten-fold cross-validation on the entire dataset, the classification accuracy for two-class classification consistently reaches 97.8% (with a specificity of 97.5%), while for five-class classification, the accuracy stably reaches 82.4% (with a specificity of 95.6%). Therefore, our classification framework can be effectively used to assist hospital doctors and medical specialists in diagnosing related diseases, especially to help accelerate the treatment of epilepsy patients.

1. Introduction

Artificial intelligence (AI), particularly machine learning (ML) and deep learning (DL), has initiated a new era of technological breakthroughs in healthcare. These advanced technologies are revolutionizing the way we handle and utilize medical data, enhancing disease classification, assisting in improving diagnostic accuracy, improving the quality of medical services, and enhancing patient treatment outcomes [1]. In recent years, there has been a surge of research combining complex networks and machine learning to diagnose diseases and distinguish sleep states. For instance, in 2017, Wang et al. proposed a method to map single-channel EEG signals into visibility graphs (VGs), including classical visibility graphs (VGs), horizontal visibility graphs (HVGs), and difference visibility graphs (DVGs). Through the use of a support vector machine (SVM) classifier, combining VGS features extracted from an EEG channel can improve seizure detection performance (the sensitivity of the benchmark feature set is $24\%$, with a false detection rate of $1.8$ times per hour; the sensitivity after combining VGS features is $38\%$, with a false detection rate of 1.4 times per hour) [2]. In 2020, Aruane et al., based on the quantile graph (QG) method, effectively distinguished healthy individuals with open and closed eyes from Alzheimer’s disease patients using five network topology measures, and the authors pointed out the best distinguishing channel, verifying the effectiveness of the QG method in analyzing complex nonlinear EEG signals [3]. Liu et al. proposed an improved quantile graph construction method based on Markov transition probability equidistant interval division strategy, which can effectively distinguish between different EEG signals [4].

In 2021, Samiei et al. proposed a new method named GraphTS, which maps EMG time series into complex networks using a visibility graph and achieves high accuracy in distinguishing between healthy and patient samples using deep neural networks [5]. In 2021, Cai et al. proposed a graph–time fusion dual-input CNN method combining complex networks and deep learning. They segmented each single-channel EEG signal into non-overlapping 30 s epochs and mapped each epoch into a limited penetrable visibility graph (LPVG) to obtain degree sequences (DSs). Finally, they combined DSs and the 30 s EEG epochs as inputs for the novel graph-time fusion dual-input CNN to detect sleep stages, achieving a classification accuracy of $87.21\%$ for six states [6]. In 2021, Veeranki et al. proposed the use of improved Hjorth features and non-parametric classifiers to classify various emotional states in skin conductance activity (EDA) signals. They found that the combination of improved Hjorth features and rotation forests achieved the highest accuracy in classifying emotional states [7]. In 2023, Vicchietti et al. applied six analysis methods, including quantile graphs and visibility graphs, to analyze EEG signals from 160 Alzheimer’s patients and 24 healthy controls. They found that methods like wavelet coherence and quantile graphs can robustly distinguish patients from healthy individuals, demonstrating their potential for non-invasive and low-cost Alzheimer’s disease detection [8].

Epilepsy is a chronic neurological disorder caused by abnormal discharges of neurons in the brain. The severe convulsions during an epileptic seizure can lead to muscle tears or other internal injuries, and patients may suddenly lose consciousness and fall. Long-term suffering from epilepsy can result in decreased self-esteem and social isolation, potentially leading to psychological issues and cognitive impairments, severely impacting the patient’s life. Therefore, the timely and accurate detection of seizures is crucial to mitigating these hazards for patients.

Machine learning has great potential in electroencephalography (EEG) test classification, and its accuracy relies heavily on feature extraction [9]. Therefore, feature extraction is crucial. Combining complex networks and machine learning, this paper proposes a feature extraction framework that uses five methods, VG, HVG, LPVG, MFDM and QGs, to transform EEG time series signals into networks. The network measures obtained from these algorithms are combined into a feature vector, which serves as the input for machine learning. Finally, we use the XGBoost machine learning algorithm to perform multi-class classification on the extracted network measures according to the categories in the dataset. In this way, we can integrate complex networks and machine learning to improve the accuracy of epilepsy disease detection.

The rest of this paper is arranged as follows: In Section 2, our methodology, including some transformation methods, i.e., the visibility graph (VG), the horizontal visibility graph (HVG), the limited penetrable visibility graph (LPVG), quantile graphs (QGs), and the modified frequency degree method (MFDM), etc., are introduced in detail. Then, within the main framework, the dataset is used in numerical experiments; some feature extraction methods, as well as the model evaluation index, are briefly introduced in Section 3. Section 4 presents the classification effect analysis on binary classification and five classification datasets. Finally, Section 5 concludes with a summary of the findings and an outlook on future research directions.

2. Methodology

2.1. Visibility Graph (VG)

Lacasa et al. introduced the first visibility graph method, known as the natural visibility graph (NVG), or simply named the visibility graph (VG) in most of the literature [10]. In the visibility graph algorithm, values of the time series are represented using vertical bars. Each data point in the time series is treated as a node in the network. If two nodes can “see” each other, there is an edge between them in the network. The visibility criterion is described as follows:

For any $(t_c,x_c)$ between two points, $(t_a,x_a)$ and $(t_b,x_b)$, here, $t_a<t_c<t_b$ if it fulfills the following relationship:

$$x_c<x_b+(x_a-x_b){\displaystyle \frac{t_b-t_c}{t_b-t_a}}$$

(1)

Then, there is an edge between the nodes corresponding to data points $(t_a,x_a)$ and $(t_b,x_b)$ after they are mapped onto the network.

The visibility graph algorithm is a method for transforming a time series into a network graph based on visibility criteria. In this algorithm, each data point in the time series is represented as a vertical bar, with the height of the bar corresponding to the value of the data point. The core principle of the algorithm is to connect nodes (bars) with an edge if they can “see” each other. Specifically, two nodes are connected by an edge if the straight line drawn between their tops does not intersect the top of any other bar that lies between them.

This visibility criterion ensures that each node is connected to all other nodes it can see, resulting in a fully connected network where each node typically has edges to at least two neighboring nodes. The visibility graph created is invariant to affine transformations, such as scaling or translation, meaning the structure of the network remains unchanged regardless of how the bars are scaled or shifted. This property makes the visibility graph a robust representation of the inherent structure of the time series data.

To better illustrate this algorithm, consider a time series with 10 data points: $0.2$, $0.5$, $0.1$, $0.8$, $0.6$, $0.75$, $0.9$, $0.3$, $0.7$, and $0.5$, sampled as a nonlinear time series, as shown in Figure 1.

From Figure 1, it can be seen that each data point is abstracted as a vertical bar, with the height of the bar corresponding to the value of the data point. If the bars can see each other, there is an edge between the corresponding data points.

2.2. Horizontal Visibility Graph (HVG)

The horizontal visibility graph algorithm was also proposed by Lacasa et al. in 2009 [11]. In this algorithm, two data points are connected by an edge in the network if they can “see” each other horizontally, meaning that the height of any intermediate data bars is less than the heights of the two data bars on either side. The visibility criterion is described as follows: For any $(t_c,x_c)$ between two points $(t_a,x_a)$ and $(t_b,x_b)$, here $t_a<t_c<t_b$, if it fulfills relationship:

$$x_a,x_b>x_c$$

(2)

then there exists a connecting edge between the corresponding two nodes.

To better illustrate this algorithm, a time series consisting of 10 sequentially emitted data points was considered, with the values being 0.2, 0.5, 0.1, 0.8, 0.6, 0.75, 0.9, 0.3, 0.7, and 0.5, respectively. Each data point is abstracted as a column, where the height of each column corresponds to the value of the respective data point. A link is established between two data points if their columns are visually connected horizontally. This representation is shown in Figure 2.

2.3. Limited Penetrable Visibility Graph (LPVG)

Based on the ideas of the visibility graph (VG), Zhou et al. proposed the Limited Penetrable Visibility Graph (LPVG) method in 2012 [12]. The fundamental idea is to determine the connection between nodes by restricting the obstruction within a limited visibility distance. Specifically, two nodes are considered connected if the number of obstructing bars between them does not exceed a specified visibility distance, L. In other words, even if there are several bars obstructing the line of sight between the nodes, as long as the number of obstructions does not exceed L, the nodes are still regarded as connected.

To further elucidate this algorithm, a time series consisting of 10 sequentially emitted data points is considered, with the values 0.2, 0.5, 0.1, 0.8, 0.6, 0.75, 0.9, 0.3, 0.7, and 0.5, respectively, as depicted in Figure 3.

2.4. Quantile Graphs (QGs)

In 2011, Campanharo et al. proposed quantile graphs (QGs), which map one-dimensional time series of $X\in T$ to $g\in G$ on a set of network graphs, where $X=\left\{x\right(t)\mid t\in \mathbb{N};x(t)\in \mathbb{R}\}$ and $g=\{N,A\}$ are the sets of nodes N (nodes) and arcs A (arcs) [13].

Firstly, a quantile parameter, Q, is defined, which represents the actual number of nodes in the generated component bitmap network. The difference between the maximum and minimum values of the time series X is divided into Q equal parts, denoted as $q_1,q_2,q_3,\dots ,q_Q$. Each measured value in X is then assigned to the block corresponding to quantile $q_i$ in these Q equal parts. Each quantile $q_i$ is assigned to a node $n_i$ in the corresponding network. Two nodes, $n_i$ and $n_j$, are then connected in the network with a weighted arc, $(n_i,n_j,w_{ij})$, where the weight, $w_{ij}$, of each arc is the transition probability in a Markov model estimated from the aggregate time series [14].

The weight, $w_{ij}^k$, is determined by the evolutionary correlation between the time series measured values $x\left(t\right)$ and $x(t+k)$, which belong to the block indices $q_i$ and $q_j$, where $t=1,2,\dots ,T$, $k=1,2,\dots ,k_{\max }<T$. The weight, $w_{ij}^k$, is evolved by the k step only. The probability of the transition between $x\left(t\right)$ in block i and $x(t+k)$ in block j determines the weight, such that larger weights between two nodes result in thicker lines in the associated network. The QG method exhibits low sensitivity to the selection of Q, where $Q\ll T$ is assumed.

After performing $l=L$ random jumps of lengths ${\delta }_{l,k}(i,j)=|i-j|$, the calculation of the average jump length $\Delta \left(k\right)$ can be described by the following equation:

$$\Delta \left(k\right)={\displaystyle \frac{1}{L}}\sum _{l=1}^L{\delta }_{l,k}(i,j)$$

(3)

where $i,j=1,2,\dots ,Q$ is a node index indicator defined by $W_k$.

The average jump length, $\Delta \left(k\right)$, can also be obtained directly from the Markov state transition matrix $W_k$, which is especially suitable for the case of many network nodes. At this time, the specific calculation formula of $\Delta \left(k\right)$ is as follows:

$$\Delta \left(k\right)={\displaystyle \frac{1}{Q}}\mathrm{tr}\left(P{W}_k^T\right)$$

(4)

where $W_k^T$ is the transpose of the state transition matrix, P is the matrix element defined by $p={\left(p_{i,j}\right)}_{Q\times Q}$, and $\mathrm{tr}(·)$ represents the matrix trace operation [14].

To better illustrate this algorithm, we provide a time series consisting of 12 points: 0.29, 0.12, 0.76, 0.35, 0.45, 0.7, 0.25, 0.12, 0.82, 0.95, 0.31, and 0.82. An example of this algorithm with $T=12,Q=4,k=1$ is shown in Figure 4.

2.5. Modified Frequency Degree Method (MFDM)

The order of time series and reproduction are two key attributes in time series analysis. In order to better mine the features of the original time series and transform the time series into a network, Li et al. proposed a frequency degree algorithm [15]. The idea of the frequency degree algorithm is that the data with high reproduction frequency will correspond to the value with magnanimity. Specifically, the frequency degree algorithm divides the time series into equidistant intervals according to the amplitude and then connects each node to its nearest left and right neighbors in time order, and then it fully connects the nodes located in the same interval. This method can preserve the amplitude and time information of the original time series.

In 2025, Niu and Liu proposed a modified frequency degree method [16] that further considers the positional information of the time series data points. Specifically, let N be the length of the time series and Q be the parameter to be input. We consider two cases: If N is divisible by Q, then the data points of the time series are evenly distributed into Q intervals. If N is not divisible by Q, then the data points of the time series are divided into $Q+1$ intervals.

The N divisible Q case: If N is evenly divided by Q, these data points will be bisected into these intervals, $d={\displaystyle \frac{N}{Q}}$, the time series will be sorted from smallest to largest, and the time series data points will be divided according to [d: d: N]; then, the data points in the same interval will be connected with its two nearest neighbors, and the data points in the same interval will be fully connected. For convenience of illustration, we present a schematic diagram of the modified frequency degree method under the condition that it can be evenly divided in Figure 5.

As shown in Figure 5, we select the time series 3, 6, 1.5, 9, 7, 8, 5, and 6, and $Q=4$ with a length of 8. Firstly, the time series is sorted, and the points on the boundary line all belong to the following smaller interval. The data points are then divided into four intervals. The first-order time series is 1.5, 3, 5, 6, 6, 7, 8, and 9, and then the corresponding position of the time series is found according to $d={\displaystyle \frac{8}{4}}=2$; that is, [2:2:8] = 2, 4, 6, and 8 corresponds to the interval limits, so the divided interval ranges are $(-\infty ,3],(3,6],(6,7],(7,9]$. So, the time series is 3, 6, 1.5, 9, 7, 8, 5, and 6, and the corresponding interval is [1, 2, 1, 4, 3, 4, 2, and 2]. Next, each data point is connected to its two nearest neighbors, and then the data points that are in the same interval are fully connected.

If N does not divide Q exactly: If N does not divide Q exactly, these data points will be divided into $Q+1$ intervals. We denote $d={\displaystyle \frac{N}{Q}}$, and the time series will be sorted from smallest to largest. The time series data points will be divided according to $⌊d:d:N⌋$, and then the data points located in the same interval will be fully connected after each data point is connected with its two nearest neighbors. In Figure 6, we provide a schematic diagram of the modified frequency degree mapping algorithm when it is not evenly divided.

As shown in Figure 6, we consider a time series of length 10: 0.27, 0.22, 0.76, 0.12, 0.82, 0.36, 0.7, 0.95, 0.25, and 0.82, with $Q=4$. First, we sort the time series in ascending order: 0.12, 0.22, 0.25, 0.27, 0.36, 0.7, 0.76, 0.82, 0.82, and 0.95. Next, compute d as follows: $d=⌊{\displaystyle \frac{N}{Q}}⌋=⌊{\displaystyle \frac{10}{4}}⌋=2$. Then, we divide the time series data points into intervals based on $[d:d:N]$, i.e., [2:2:10] = 2, 4, 6, 8, and 10. The intervals are as follows: $(-\infty ,0.22]$, (0.22, 0.27], (0.27, 0.7], (0.7, 0.82], and (0.82, 0.95]. Thus, the time series of 0.27, 0.22, 0.76, 0.12, 0.82, 0.36, 0.7, 0.95, 0.25, and 0.82, corresponds to the following interval indices: [2, 1, 4, 1, 4, 3, 3, 5, 2, 4]. Finally, we connect each data point to its two nearest neighbors, and we fully connect all data points within the same interval.

According to the literature [15], when the length range of a given time series is 1000 to 10,000, it may be appropriate to select a Q equal to 128 or 256. Therefore, $Q=128$ is selected in this paper.

3. Main Framework, Dataset, and Feature Extraction Overview

3.1. Main Framework

This paper first converts EEG signals into corresponding associated networks using five different methods: VG, HVG, LPVG, MFDM, and QG. For each algorithm, the related network measures of the associated networks are all firstly calculated. Then, features with a significance level greater than $0.05$ are filtered out using ANOVA. The remaining network features are concatenated into a vector and input into the XGBoost classifier for classification. The main framework process of this paper is shown in Figure 7.

3.2. Dataset Used in Numerical Experiments

In this study, we utilize the artifact-free EEG database provided by the University of Bonn, which is freely available online [17]. This database has been widely used for EEG feature extraction and classification in the literature [18]. Our dataset comprises five distinct sets, labeled A, B, C, D, and E. Each set contains 100 single-channel EEG segments, each segment lasting $23.6$ s and sampled at a rate of $173.61H_z$. Sets A and B consist of surface EEG recordings from healthy, awake volunteers, with Set A containing recordings taken while the volunteers had their eyes open and Set B containing recordings taken with their eyes closed. Sets C and D contain intracranial EEG signals from epileptic patients recorded during seizure-free intervals, with Set C containing recordings from the hippocampal formation in the opposite hemisphere of the brain and Set D containing recordings from the epileptogenic zone. Set E includes intracranial EEG signals recorded at sites exhibiting ictal activity, representing seizure activity. Figure 8 illustrates sample EEG segments from sets A, B, C, D, and E. There are five data subsets, each containing 100 brain telecom number segments and 4097 data points. The data have been filtered according to related literature published in the last several decades (i.e., we chose to filter broadband in 0.53–40$H_z$. This range covers most of the EEG frequency components associated with cognitive activity, such as $\alpha$ waves (8–12$H_z$) and $\beta$ waves (13–30$H_z$)), and the specific state diagram of different types of EEG signals can be seen in Figure 8.

3.3. Feature Extraction

In this process, extracting features from EEG signals is crucial, as they carry different information, depending on whether the subject is healthy or epileptic and whether they are in a seizure or non-seizure state. Initially, EEG time series are transformed into associated networks using various methods. The adjacency matrix of each network is stored, and the average degree, average clustering coefficient, density, network diameter, global efficiency, and average path length are calculated for networks under five different algorithms: the VG, the HVG, the LPVG, MFDM, and the QG [19,20,21]. Additionally, the average jump length $\Delta$ is computed for networks under the QG algorithm [13]. The network measures obtained from each algorithm are then standardized. Subsequently, an analysis of variance (ANOVA) is used to filter out columns with significance levels greater than $0.05$. In statistics, $0.05$ is often used as a standard threshold to determine whether a result is statistically significant. Choosing $0.05$ as the significance level means that, if the p-value of a feature is less than $0.05$, it is considered that the feature has a significant impact on the classification task. On the contrary, it is considered that the influence is not significant. This selection was based on balancing considerations in statistical conventions and practical applications, aiming to include as many features useful for classification as possible while controlling for false positive rates. The strength of ANOVA is its simplicity and intuitiveness, which directly assesses the relationship between features and labels and is effective in many cases.

As shown in Algorithm 1, the ANOVA feature concatenation method selects significant features based on their p-values. This method is effective in reducing the dimensionality of the dataset by retaining only those features that have a statistically significant impact on the target variable.

Algorithm 1 ANOVA feature concatenation

1: Input: Dataset $X\in {\mathbb{R}}^{m\times n}$, labels $Y\in {\mathbb{R}}^m$, significance threshold $\alpha =0.05$ 2: Output: Concatenated feature set $X_{\mathrm{selected}}$ 3: Initialize empty list $\mathrm{selected}\_\mathrm{features}$ 4: for each feature $f_i$ in X do 5:       Perform ANOVA to compute p-value $p_i$ for feature $f_i$ 6:       if $p_i<\alpha$ then 7:            Append feature $f_i$ to $\mathrm{selected}\_\mathrm{features}$ 8:       end if 9: end for 10: Concatenate the selected features into a new set, $X_{\mathrm{selected}}$ 11: Return  $X_{\mathrm{selected}}$

The remaining network measures for each algorithm are concatenated into a single vector. These vectors are combined to form a feature matrix, which is then used as input for traditional classification machine learning models.

Through an analysis of variance, we filter out the network diameter feature for both VG and LPVG. The final selected features for each algorithm are listed as follows:

• VG: average degree (${\alpha }_{VG}$); the maximum degree($M_{VG}$); average clustering coefficient ($C_{VG}$); density: (${\rho }_{VG}$); global efficiency: ($G_{VG}$); and average path length: ($L_{VG}$).
• HVG: average degree (${\alpha }_{HVG}$); the maximum degree ($M_{HVG}$); average clustering coefficient ($C_{HVG}$); density: (${\rho }_{HVG}$); global efficiency: ($G_{HVG}$); network diameter ($D_{HVG}$); and average path length: ($L_{HVG}$).
• LPVG: average degree (${\alpha }_{LPVG}$); the maximum degree ($M_{LPVG}$); average clustering coefficient ($C_{LPVG}$); density: (${\rho }_{LPVG}$); global efficiency: ($G_{LPVG}$); and average path length: ($L_{LPVG}$).
• MFDM: average degree (${\alpha }_{MFDM}$); the maximum degree ($M_{MFDM}$); average clustering coefficient ($C_{MFDM}$); density: (${\rho }_{MFDM}$); global efficiency: ($G_{MFDM}$); network diameter ($D_{MFDM}$); average path length: ($L_{MFDM}$).
• QG: and average jump length ($\Delta$).

Remark 1.

For the QG algorithm, the most representative feature, namely the average jump length, is selected. As suggested by the literature [4], when $Q=30$ and $k=4$, significant differentiation is observed within the dataset. Hence, we chose $Q=30$ and $k=4$. The corresponding box plot is presented in Figure 9.

The feature vector $V_{\mathrm{EEG}\mathrm{signals}}$ is constructed using multiple-measures composited strategies and is typically described as follows:

$$V_{\mathrm{EEG}\mathrm{signals}}=\left[{\alpha }_{\mathrm{VG}},\dots ,L_{\mathrm{VG}},{\alpha }_{\mathrm{HVG}},\dots ,L_{\mathrm{LPVG}},{\alpha }_{\mathrm{MFDM}},\dots ,L_{\mathrm{MFDM}},{\Delta }_{\mathrm{QG}}\right]$$

Therefore, the feature vector $V_{\mathrm{EEG}\mathrm{signals}}$ is composed of twenty-seven network measures used for subsequent classification tasks.

3.4. Model Evaluation Index

In order to facilitate the evaluation in the following article, we first give some definitions of evaluation indicators and cross-validation listed as below. Related indicators are introduced in the literature [22,23,24,25].

Accuracy: Accuracy is the ratio of the number of correct predictions to the total number of predictions. It reflects how often the classifier is correct across all classes.

Balanced accuracy: Balanced accuracy measures model performance on imbalanced datasets. It is the average of the recall rates for each class, providing a more accurate reflection of the model’s ability to recognize the minority class. Balanced accuracy values range from 0 to 1, with 1 being the best.

$F_1$-Score: The F1-score is the harmonic mean of precision and recall, representing the overall effectiveness of the model in classification tasks. It balances the trade-off between precision and recall, especially in cases of class imbalance.

Specificity: Specificity measures the proportion of actual negatives correctly identified as negatives. In multiclass classification, it is calculated for each class as the proportion of actual non-class samples correctly identified as non-class.

True negatives (TNs): true negatives for class i are the count of actual non-class i samples correctly predicted as non-class i.

False positives (FPs): false positives for class i are the count of actual non-class i samples incorrectly predicted as class i.

Precision: precision is the proportion of predicted positive samples that are actually positive, reflecting the accuracy of positive predictions.

Recall: recall is the proportion of actual positive samples correctly predicted as positive, indicating the model’s ability to identify relevant positive samples.

Matthews correlation coefficient (MCC): MCC is a balanced classification metric ranging from $[-1,1]$, measuring the quality of binary classifications by considering true and false positives and negatives.

Cohen’s kappa: Cohen’s kappa assesses agreement between the classifier and a random classifier, adjusting for chance agreement for a nuanced evaluation.

Hamming loss: Hamming loss represents the proportion of incorrectly classified samples, measuring the average number of misclassified labels.

Jaccard index: the Jaccard index, or intersection over union (IoU), evaluates classifier accuracy by comparing the intersection and union of predicted and actual sets.

Cross-validation: Cross-validation involves dividing the dataset into k subsets, using $k-1$ subsets for training and 1 for testing in each iteration. This process is repeated k times, with each subset serving as the test set once, and the results are aggregated for final evaluation.

4. Classification Effect on the Dataset

In this paper, we use the XGBoost classifier (i.e., XGBClassifier) to classify EEG data and evaluate our method’s performance. XGBoost (eXtreme Gradient Boosting) is an enhanced machine learning model suitable for regression, classification, and ranking problems. This model is based on the gradient boosting algorithm, which improves the overall predictive performance by iteratively building and combining multiple weak classifiers [26]. Specifically, we first normalize the feature data so that the mean is 0 and the standard deviation is 1. Then, we set the parameters of the XGBoost classifier. After that, we use stratified cross-validation (StratifiedKFold) to divide the data into ten folds, with nine folds used for training and one fold used for validation. The performance of the XGBoost classifier on the given EEG dataset is evaluated through 10-fold cross-validation. We conduct experiments using our framework on both binary classification and five-class classification tasks. For each individual method, the final selected network features are as follows: For VG, HVG, LPVG, and MFDM, the following seven network measures were selected: average degree, maximum degree, average clustering coefficient, network density, network diameter, global efficiency, and average path length. For QG, the average jump length was selected.

Our method involves concatenating the network measures obtained from each of the aforementioned algorithms into a long vector. We then use ANOVA to assess the relationship between each feature and the labels, selecting the features that have a significant impact on the classification task. The p-value for each feature indicates whether there is a significant difference in the mean across different categories. If the p-value is greater than $0.05$, it suggests that the feature does not have a significant impact on the classification task, and thus, the feature is discarded. The p-value of the computed features are shown in

Table 1. The p-value of the computed features in our numerical experiments.

Feature	p-Value
${\rho }_{VG}$	$5.47167\times {10}^{-38}$
$D_{VG}$	$5.44559\times {10}^{-1}$
$M_{VG}$	$3.59848\times {10}^{-24}$
${\alpha }_{VG}$	$5.47167\times {10}^{-38}$
$C_{VG}$	$6.75227\times {10}^{-77}$
$L_{VG}$	$2.50911\times {10}^{-2}$
$G_{VG}$	$1.13543\times {10}^{-18}$
${\rho }_{HVG}$	$1.59894\times {10}^{-93}$
$D_{HVG}$	$9.96596\times {10}^{-65}$
$M_{HVG}$	$1.25973\times {10}^{-32}$
${\alpha }_{HVG}$	$1.59894\times {10}^{-93}$
$C_{HVG}$	$3.52079\times {10}^{-71}$
$L_{HVG}$	$1.73161\times {10}^{-82}$
$G_{HVG}$	$8.53595\times {10}^{-99}$
${\rho }_{LPVG}$	$1.51657\times {10}^{-46}$
$D_{LPVG}$	$8.10539\times {10}^{-1}$
$M_{LPVG}$	$6.97230\times {10}^{-24}$
${\alpha }_{LPVG}$	$1.51657\times {10}^{-46}$
$C_{LPVG}$	$4.33977\times {10}^{-94}$
$L_{LPVG}$	$1.77361\times {10}^{-3}$
$G_{LPVG}$	$1.87006\times {10}^{-14}$
${\rho }_{MFDM}$	$4.01871\times {10}^{-12}$
$D_{MFDM}$	$9.98876\times {10}^{-10}$
$M_{MFDM}$	$5.32264\times {10}^{-8}$
${\alpha }_{MFDM}$	$4.01871\times {10}^{-12}$
$C_{MFDM}$	$3.14236\times {10}^{-8}$
$L_{MFDM}$	$4.56050\times {10}^{-8}$
$G_{MFDM}$	$1.13674\times {10}^{-10}$
${\Delta }_{QG}$	$1.55180\times {10}^{-130}$

.

After calculation, we find that the p-value of the network diameter feature under the VG and LPVG methods are $0.54$ and $0.81$, respectively, so we filter out the network diameter feature for both the VG and LPVG methods. Additionally, we observe that removing any feature would lead to a decrease in classification accuracy, negatively impacting the classification task. Therefore, we select these 27 features as the feature vector, as they can more comprehensively capture the intrinsic characteristics of the signal.

Remark 2.

A 27-dimensional feature vector filtered via an ANOVA reduces redundancy while retaining discriminative power. The average jump length, ${\Delta }_{QG}$, from $QG$ contributes most significantly to class separation.

4.1. Classification Effect on Binary Classification Dataset

XGBoost has achieved remarkable results in many fields, so we want to use this model to classify epilepsy. In epilepsy detection, a high-precision model can distinguish between epilepsy patients and healthy people, helping doctors quickly and accurately determine whether patients have specific diseases and thereby accelerating the treatment process. Through automated and intelligent binary classification, decision-making efficiency can be significantly improved, and the time and cost of manual judgment can be reduced. Therefore, we first evaluated the effect of the framework proposed in this article on binary classification tasks. We first performed a binary classification by grouping A (healthy, eyes open) and B (healthy, eyes closed) as one category, labeled as Class 1. C (epileptic, opposite zone), D (epileptic, epileptogenic zone), and E (epileptic, seizure) were grouped together as another category, labeled as Class 2. The classification was performed using the XGBoost model. The performance of the model is summarized in

Table 2. Model evaluation indicators in binary classification task.

Method	Accuracy	Balanced Accuracy	F1 Score	Precision	Recall	Specificity	MCC	Cohen’s Kappa	Hamming Loss	Jaccard Index
VG	0.882	0.879	0.901	0.908	0.893	0.865	0.755	0.755	0.118	0.820
HVG	0.934	0.931	0.945	0.944	0.947	0.915	0.862	0.862	0.066	0.896
LPVG	0.928	0.928	0.939	0.952	0.927	0.930	0.851	0.851	0.072	0.885
MFDM	0.840	0.833	0.867	0.864	0.870	0.795	0.666	0.666	0.160	0.765
QG	0.796	0.784	0.832	0.821	0.843	0.725	0.572	0.572	0.204	0.713
Ours	0.978	0.978	0.982	0.983	0.98	0.975	0.954	0.954	0.020	0.964

, which presents several evaluation metrics. The confusion matrix diagram and ROC curve of the XGBoost model on the binary classification task are plotted in Figure 10 and Figure 11, respectively.

Although the individual classification algorithms do not exhibit high accuracy, the performance improves significantly after applying the feature concatenation method based on ANOVA. The results demonstrate that our feature extraction framework, when coupled with the XGBoost model, yields excellent performance across various evaluation metrics. The classification performance of various algorithms was compared, and the results show that our method outperforms others on multiple evaluation metrics. The balanced accuracy achieved was $0.978$, indicating that the model has strong performance across both classes. The specificity reached $97.5\%$, demonstrating that the model is highly effective in identifying non-positive samples. The F1 score of $0.982$ further emphasizes that the model maintains a good balance between precision and recall, while the precision value of $0.983$ indicates that the model is highly accurate in predicting positive cases. The recall rate of $0.980$ reflects the model’s ability to correctly identify positive samples. Furthermore, the Matthews correlation coefficient (MCC) and Cohen’s kappa coefficient, both at $0.954$, suggest that the model’s predictions are significantly better than random chance. The Hamming loss of $0.020$ indicates that only $2\%$ of the samples were misclassified, while the Jaccard index of $0.964$ confirms a high level of agreement between predicted and actual results. These findings highlight the effectiveness and robustness of our feature extraction framework when used in conjunction with the XGBoost model. To further evaluate the impact of different classifiers on classification results, we performed experiments using MATLAB’s Classification Learner tool (after sorting). The results are summarized in

Table 3. Results of different classifiers on binary classification tasks.

Rank	Model Type	Accuracy (%)	Total Cost	Preset	Prediction Speed (obs/s)	Training Time (s)
1	Ensemble	97.6	12	Custom Ensemble	274.21	168.61
2	SVM	97.4	13	Custom SVM	20,898.55	41.13
3	Ensemble	97.4	13	Bagged Trees	2703.39	3.53
4	Neural Network	97.2	14	Custom Neural Network	17,686.34	165.26
5	Tree	97.2	14	Custom Tree	13,993.02	17.42
6	SVM	97.2	14	Cubic SVM	14,767.65	1.11
7	Kernel	97.2	14	SVM Kernel	17,235.55	1.84
8	Neural Network	97.0	15	Trilayered Neural Network	17,110.86	1.03
9	Tree	96.8	16	Fine Tree	22,969.39	1.72
10	Tree	96.8	16	Medium Tree	21,404.11	3.76
11	SVM	96.8	16	Medium Gaussian SVM	12,757.80	2.04
12	Ensemble	96.8	16	RUSBoosted Trees	6180.08	2.12
13	Ensemble	96.6	17	Subspace KNN	924.60	3.72
14	Neural Network	96.6	17	Medium Neural Network	21,523.24	4.87
15	SVM	96.4	18	Quadratic SVM	15,984.76	1.40
16	KNN	96.2	19	Custom KNN	4506.50	18.77
17	KNN	96.2	19	Fine KNN	7484.53	3.06
18	Neural Network	96.2	19	Narrow Neural Network	16,441.53	1.68
19	Neural Network	96.2	19	Wide Neural Network	22,565.42	1.03
20	Neural Network	96.2	19	Bilayered Neural Network	20,544.01	1.62
21	KNN	96.0	20	Weighted KNN	8537.68	2.07
22	Kernel	96.0	20	Logistic Regression Kernel	16,205.77	1.09
23	Tree	95.8	21	Coarse Tree	16,004.92	2.09
24	SVM	95.8	21	Linear SVM	12,219.59	2.11
25	Logistic Regression	95.4	23	Logistic Regression	4623.44	3.51
26	KNN	95.2	24	Medium KNN	7554.55	1.69
27	Naive Bayes	94.8	26	Custom Naive Bayes	2382.31	63.52
28	Naive Bayes	94.8	26	Kernel Naive Bayes	1967.08	3.54
29	KNN	94.8	26	Cosine KNN	7863.22	0.83
30	SVM	94.6	27	Fine Gaussian SVM	12,950.65	0.79
31	KNN	94.6	27	Cubic KNN	5804.98	0.95
32	Discriminant	92.4	38	Custom Optimizable Discriminant	9477.07	28.42
33	Naive Bayes	92.4	38	Gaussian Naive Bayes	4518.48	3.67
34	SVM	91.2	44	Coarse Gaussian SVM	14,743.48	1.92
35	Ensemble	90.6	47	Subspace Discriminant	1371.42	3.28
36	Discriminant	89.4	53	Linear Discriminant	12,721.64	1.16
37	KNN	86.6	67	Coarse KNN	7719.47	2.57
38	Ensemble	60.0	200	Boosted Trees	19,922.38	2.83

, which presents the performance of various classifiers in binary classification tasks. To make it easier to see which are the top 10 models of the Matlab2023b classification toolbox in the binary classification task, we visualized them in Figure 12. We compared the method in this paper with the popular EEG classification model CNN method based on deep learning, and from Figure 13, we found that the test set accuracy of the CNN method on the binary classification task was 0.93, which was not as high as the accuracy of the method proposed in this paper. This can illustrate the effectiveness of our method. The confusion matrix under the CNN method is shown in Figure 14. Therefore, our framework performs well across all indicators of the binary classification tasks.

4.2. Classification Effect on Five Classification Datasets

In this article, the five-category classification of EEG signals can more finely distinguish between healthy states and different states of epilepsy. The five-category classification task helps doctors make more detailed divisions of patients’ disease states, thereby formulating more personalized treatment plans. In epilepsy treatment, understanding the patient’s specific seizure type and brain area activity is crucial to choosing appropriate drugs and surgical strategies. Through the five-category classification, we can more deeply analyze the differences and connections between different disease states and provide data support for the exploration of disease mechanisms and innovation of treatment methods. Therefore, the five-class classification was then performed. The evaluation metrics for both the single-method XGBoost model and our method obtained using Python are as follows in

Table 4. Model evaluation indicators in the five-class classification task.

Method	Accuracy	Balanced Accuracy	F1 Score	Precision	Recall	Specificity	MCC	Cohen’s Kappa	Hamming Loss	Jaccard Index
VG	0.568	0.568	0.571	0.576	0.568	0.892	0.460	0.460	0.432	0.406
HVG	0.728	0.728	0.728	0.729	0.728	0.932	0.660	0.660	0.272	0.592
LPVG	0.594	0.594	0.596	0.603	0.594	0.899	0.493	0.493	0.406	0.430
MFDM	0.470	0.470	0.469	0.469	0.470	0.868	0.338	0.338	0.530	0.309
QG	0.438	0.438	0.436	0.435	0.438	0.860	0.298	0.298	0.562	0.291
Ours	0.824	0.824	0.823	0.823	0.824	0.956	0.780	0.780	0.176	0.715

. The confusion matrix diagram and ROC curve of the XGBoost model on the five classification tasks are plotted in Figure 15 and Figure 16, respectively.

Although the classification accuracy of individual algorithms is relatively low, the performance metrics for the five-class classification are significantly improved after applying the feature concatenation method based on ANOVA. It is observed that our feature extraction framework performs well across various performance indicators when classified with the XGBoost model. The balanced accuracy is 0.824, demonstrating that the model performs consistently across all classes, with an overall accuracy of 82.4%. The specificity reaches 95.6%, indicating the model’s strong ability to correctly identify non-target samples for each class. The $F_1$ score is also 0.823, highlighting a good balance between precision and recall. Both the accuracy and recall rates stand at 0.824, showing the model’s reliability in predicting positive samples and effectively identifying most of the actually positive cases. The precision value of 0.823 indicates that the model is highly accurate in predicting positive cases. The Matthews correlation coefficient (MCC) and Cohen’s Kappa coefficient are both 0.780, suggesting that the model’s prediction quality is significantly better than random guessing. The Hamming loss is 0.176, meaning 17.6% of the samples were misclassified, while the Jaccard index is 0.715, indicating a 71.5% similarity between the predicted and actual results.

In summary, the XGBoost model demonstrates excellent performance across multiple metrics, proving to be both robust and effective on this dataset. A comparison of other machine learning methods using MATLAB’s Classification Learner is presented as follows (after sorting) in

Table 5. Results of different classifiers in five classification tasks.

Rank	Model Type	Accuracy (%)	Total Cost	Preset	Prediction Speed (obs/s)	Training Time (s)
1	SVM	82.0	90	Custom SVM	10,505.95	249.81
2	SVM	81.2	94	Linear SVM	3907.47	4.57
3	Ensemble	81.0	95	Custom Ensemble	3021.87	88.07
4	SVM	80.8	96	Quadratic SVM	3794.01	4.37
5	Neural Network	80.6	97	Custom Neural Network	21,322.14	261.35
6	Neural Network	80.6	97	Medium Neural Network	10,889.95	4.83
7	Neural Network	80.0	100	Wide Neural Network	22,057.92	2.10
8	Ensemble	79.2	104	Bagged Trees	2281.52	5.26
9	SVM	79.0	105	Cubic SVM	3244.70	4.26
10	SVM	78.6	107	Medium Gaussian SVM	2875.67	4.03
11	Ensemble	78.2	109	Boosted Trees	2966.54	3.95
12	Tree	77.8	111	Fine Tree	5292.95	8.34
13	Tree	77.8	111	Custom Tree	8286.84	25.31
14	Neural Network	77.8	111	Narrow Neural Network	13,850.45	5.43
15	Neural Network	77.6	112	Trilayered Neural Network	14,166.03	7.04
16	Neural Network	77.4	113	Bilayered Neural Network	13,540.19	5.83
17	KNN	76.8	116	Custom KNN	6235.37	26.83
18	Kernel	76.4	118	Custom Kernel	5609.94	10.26
19	Ensemble	74.8	126	Subspace Discriminant	1279.07	4.06
20	KNN	74.6	127	Weighted KNN	4769.25	2.09
21	Kernel	74.6	127	Custom Kernel	5119.61	5.70
22	Tree	74.4	128	Medium Tree	11,200.87	0.97
23	Ensemble	74.2	129	RUSBoosted Trees	2949.14	3.89
24	Ensemble	73.8	131	Subspace KNN	893.56	5.70
25	Discriminant	72.2	139	Optimizable Discriminant	7123.51	30.54
26	Discriminant	72.2	139	Linear Discriminant	11,343.24	3.04
27	Naive Bayes	71.6	142	Custom Naive Bayes	967.91	111.53
28	Naive Bayes	71.6	142	Custom Naive Bayes	822.89	7.32
29	KNN	71.6	142	Fine KNN	5459.71	3.28
30	KNN	71.0	145	Cosine KNN	4489.38	2.32
31	SVM	70.4	148	Coarse Gaussian SVM	5785.77	5.28
32	KNN	70.0	150	Medium KNN	4529.33	1.64
33	KNN	69.0	155	Cubic KNN	3553.80	2.20
34	Naive Bayes	67.0	165	Gaussian Naive Bayes	2288.75	2.76
35	SVM	67.0	165	Fine Gaussian SVM	2990.76	4.15
36	Tree	65.2	174	Coarse Tree	11,090.56	3.89
37	KNN	58.6	207	Coarse KNN	4593.06	1.23

. To make it easier to see which are the top 10 models of the Matlab R2023b classification toolbox in the five classification tasks, we have made a visualization in Figure 17. Therefore, our framework performs well on all indicators of the five classification tasks.

We compared the method in this paper with the popular EEG classification model CNN method based on deep learning, and from Figure 18, we found that the test set accuracy of the CNN method on the five classification task was 0.67, which was not as high as the accuracy of the method proposed in this paper. This can illustrate the effectiveness of our method. The confusion matrix under the CNN method is shown in Figure 19. Therefore, our framework performs well across all indicators of the five classification tasks.

From Table 5, it can be seen that, using XGBoost, the framework performs well across various metrics in the five-class classification task, with the highest classification accuracy achieved.

5. Conclusions and Outlook

In this paper, a multi-network feature-fusion framework integrating five complex network transformation methods (the VG, the HVG, the LPVG, MFDM, and the QG) has been proposed for epileptic EEG classification. The VG and the HVG capture local temporal patterns, the QG quantifies long-range transition properties, and MFDM enhances sensitivity to amplitude distributions. This fusion overcomes the limitations of single-algorithm approaches. The experimental results demonstrate that the proposed framework achieves an accuracy of $97.8\%$ and a specificity of $97.5\%$ in binary classification tasks, with a balanced accuracy of $97.8\%$ and an F1 score of $0.982$. These results highlight the model’s ability to effectively distinguish between healthy and epileptic EEG signals. The Matthews correlation coefficient and Cohen’s kappa coefficient, both at $0.954$, further confirm the model’s superior predictive quality compared to random guessing. In the more complex five-class classification task, the framework achieves an accuracy of $82.4\%$ and a specificity of $95.6\%$. The balanced accuracy of $82.4\%$ and an F1 score of $0.823$ indicate that the model maintains a good balance between precision and recall across multiple classes. The Matthews correlation coefficient and Cohen’s Kappa coefficient, both at $0.780$, demonstrate the model’s effectiveness in handling multi-class classification. The proposed framework exhibits robust performance in both binary and five-class classification tasks, demonstrating high accuracy and specificity and thereby validating its effectiveness.

The framework eliminates the need for complex signal preprocessing or deep learning infrastructure, making it well-suited for resource-constrained medical environments while providing real-time diagnostic support for clinicians. Additionally, its efficient implementation reduces computational demands. However, there are also some limitations. For example, the amount of data in this paper is not large, and the data are only verified on classic datasets. Future studies will expand the experiment by incorporating multi-center clinical data (such as the CHB-MIT dataset). Since the method of this paper requires converting the time series into a network before calculating the feature classification, it is more applicable to time series with a length of less than $10,000$. The framework of this paper can be used to obtain results conveniently and quickly, but if the amount of data is too large, the calculation may be slower. Therefore, for large-scale EEG data, we can use deep learning models for classification in the future. For example, converting time series data into images for the training of convolutional neural networks (CNNs) is a promising way to improve classification performance. Other methods for converting time series into network graphs can also be explored, and then graph neural network (GNN)-based methods can be used to effectively mine topological features from the network representation of time series data for classification. In addition, it is also possible to consider integrating time–frequency imaging techniques, such as continuous wavelet transform, which can further improve classification performance by capturing more discriminative features, which are essential for accurate diagnosis of epilepsy. Although the proposed framework does not require complex signal preprocessing or deep learning infrastructure, making it suitable for resource-limited settings, its future adaptability may include real-time epilepsy detection in clinical settings. Further validation using real-world data, especially integrating the framework with wearable EEG devices, will enhance its practicality and solidify its role as a reliable tool for providing real-time diagnostic support to clinicians. In summary, while the proposed framework exhibits strong performance and practicality, several opportunities remain to expand its applicability. Future research will focus on addressing its limitations, exploring advanced techniques, and expanding its applicability to various clinical scenarios, solidifying its role as a reliable tool for automated diagnosis in resource-limited healthcare settings.